Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21425870 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21425700 | C2 | semidirect |
| 5. #21425004 | C2 | semidirect |
| 6. #21424995 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 11. C2×#14273670 | C4 | semidirect |
| 12. C2×#14273668 | C4 | semidirect |
| 164. #2143 | D59 | semidirect |
| 194. C59 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| #21425870 | 2 |
| #21425813 | 2 |
| #21425700 | 2 |
| #21425004 | 2 |
| #21424995 | 2 |
| C59×#2143 | 2 |
| #13247 | 59 |